Application of the maximum entropy method in texture analysis

The problem of estimating the crystallite orientation distribution function (codf) based on the leading texture coefficients is considered. Problems of such a type are called moment problems, which are well known in statistical mechanics and other areas of science. It is shown how the maximum entropy method can be applied to estimate the codf. Special emphasis is given to a coordinate-free formulation of the problem. The codf is represented by a tensorial Fourier series. The equations, which have to be solved for the estimate of the distribution function, are derived for all tensor ranks of the Fourier coefficients. As a numerical example, a model codf is estimated based on a set of discrete crystal orientations given by a full-constrained Taylor type texture simulation.